Yes, it is possible. You need to first convert ethanol into acetic acid through oxidation followed by treatment with ammonia which will give ethanamide. The Hoffman bromamide degradation of ethanamide will yield methyl amine which can be transformed into methanol by treating with nitrous acid.
A process for converting methanol to ethanol which comprises reacting methanol and carbon monoxide in the presence of a catalyst to produce a product comprising at least 25 mole % methyl acetate and, in some instances, acetic acid. The acetic acid then is reacted with at least one alcohol to produce at least one acetate selected from methyl acetate, ethyl acetate, and butyl acetate. The at least one acetate (if produced) and the methyl acetate produced as a result of reacting methanol and carbon monoxide then are hydrogenated to produce ethanol. Syngas may be produced from biomass to produce all or a portion of the methanol, hydrogen, and carbon monoxide requirements for the process.
Currently, most methanol is produced by the catalytic conversion of syngas (a mix of carbon monoxide, carbon dioxide and hydrogen) from fossil sources. Information on methanol use is available from the International Methanol Producers and Consumers Association IMPCA and from the Methanol Institute.
So if you have ethanol you can hydrolyse it first to CO and H2 and then from CO and H2, you can produce methanol by usibng a bi functional catalyst Cu-Zn-Al2O3 with high pressure (40 bar) at temperature 200-300 Celsius